The victory restored the table-toppers four point lead over Barcelona, setting up for them the chance to be crowned LaLiga champions on Thursday, if they beat visiting Villarreal.
If they were able to see off Villarreal, Madrid would win just their second La Liga title in eight seasons and their 34th overall.
The victory over Granada at Los Carmenes on Monday was hard-fought and hard-won.
Goals from Ferland Mendy – his first for the club – and Karim Benzema gave Madrid a first half advantage.
Mendy slammed home a brilliant finish from a tight angle to become the 21st Madrid player to score in LaLiga this season.
Benzema increased his top-flight tally this term to 19 as he made it 2-0.
Although Darwin Machis pulled one back five minutes into the second half, Madrid survived a couple of late scares to make it nine straight victories and edge closer to LaLiga title.
AFP